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@inproceedings{948678,
author = {Brázdil, Tomáš and Krčál, Jan and Křetínský, Jan and Řehák, Vojtěch},
address = {Berlin Heidelberg New York},
booktitle = {CONCUR 2011 - Concurrency Theory: 22nd International Conference},
keywords = {generalized semi-Markov processes; long-run average; stability; discrete events},
howpublished = {tištěná verze "print"},
language = {eng},
location = {Berlin Heidelberg New York},
isbn = {978-3-642-23216-9},
pages = {140-155},
publisher = {Springer},
title = {Fixed-delay Events in Generalized Semi-Markov Processes Revisited},
year = {2011}
}
TY - JOUR
ID - 948678
AU - Brázdil, Tomáš - Krčál, Jan - Křetínský, Jan - Řehák, Vojtěch
PY - 2011
TI - Fixed-delay Events in Generalized Semi-Markov Processes Revisited
PB - Springer
CY - Berlin Heidelberg New York
SN - 9783642232169
KW - generalized semi-Markov processes
KW - long-run average
KW - stability
KW - discrete events
N2 - We study long run average behavior of generalized semi-Markov processes with both fixed-delay events as well as variable-delay events. We show that allowing two fixed-delay events and one variable-delay event may cause an unstable behavior of a GSMP. In particular, we show that a frequency of a given state may not be defined for almost all runs (or more generally, an invariant measure may not exist). We use this observation to disprove several results from literature. Next we study GSMP with at most one fixed-delay event combined with an arbitrary number of variable-delay events. We prove that such a GSMP always possesses an invariant measure which means that the frequencies of states are always well defined and we provide algorithms for approximation of these frequencies. Additionally, we show that the positive results remain valid even if we allow an arbitrary number of reasonably restricted fixed-delay events.
ER -
BRÁZDIL, Tomáš, Jan KRČÁL, Jan KŘETÍNSKÝ and Vojtěch ŘEHÁK. Fixed-delay Events in Generalized Semi-Markov Processes Revisited. In \textit{CONCUR 2011 - Concurrency Theory: 22nd International Conference}. Berlin Heidelberg New York: Springer. p.~140-155. ISBN~978-3-642-23216-9. 2011.
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